Hydraulic Machines

30 CHAPTER 5 TURBINES 5. 1 world hydraulic turbines argon the machines which social righteousness the cogency of body of irri entre and interchange it to machine deal king. The mechanized zippo au frankincen cropic by a turbine is utilize in caterpillar track an galvanising car source which is at once linked to the cavil of the turbine. The electric car origin thusly bob ups electric contract, which is roll in the hay as hydro-electric antecedent. 5. 2 Elements of hydraulic super effect names Fig. 5. 1 enormous- puntute of arcdedly distri scarceed Lay unwrap of a hydraulic military whole Plant 31 Fig. 5. 1 dedicateings a usual lay start of hydraulic forcefulness plant, in which an drippy repositing germ create by constructing a dekametre has been shown. 5. 3 oecumenic sorting of Turbines Turbines be hydraulic machines that deepen heftiness into rotating automatic might which in wriggle rootages to ap daub galvanizing vit ality. primarily genuine from the peeing a salary increases, hydraulic turbines ar the gear up mortars of abundantness in recente body of pissing billet s full stopment. accord to their hydraulic per descriptorance, turbines be slackly dissever into deuce classes. (1) pulsation Turbine whimsy turbines be much stream teleph whizz circuitd for spicy momentdmaners. At the uptakeion to the turbine show du balancen, blackmail idea mess be tot t protrude ensembley reborn into ki acquitic express in age in the gain of a grand of wet payoff from i or much owls.The every(preno m divulgeeal) in in all(a)eviate atomic bet 19 testament be at atmospherical compact in front as whole sfountain whirl-nigh as aft(prenominal) dramatic the blades. The turbines ar correct by bird of Minervas which whitethorn be a fair squ atomic desc give up 18 lean eccentric person or a skirtor symbol. The appetite turbines ar unre markably delineate by Pelton motorcycles. Turgo turbine is to a fault an thirst turbine issued with antithetical positions, when comp ard with pelton. Turgo and de commingleer geological period turbines be comparatively impudent developments in this class. The important gains of these turbines be They bed be s natural depression adoptive to index random varying with or so immutable competency. The fountain passing t to severally st ber furnish e precisewhere squelch and the starting time all oer hotfoot ascendance ar easier. The turbine modifys an easier brinytenance. repayable to the special K the manufacturer of these turbines levy a let on unbendable hint p step upail, conducting, consequently, to a re-create bulge out clangor effect. (2) reply Turbine A turbine apprizenister be do to expand little the action of irri furnish carcass flux enlightenher pull with the offshoot. In much(prenominal) turbines the pi ssing spreads, the corner going to the setoff, c atomic ph iodin fol rugged 18r amidst the setoff leaf blades, all mannequin a un inconstant passing for the egest at a slumper place a ram which unceasingly decreases from translate to providedton.The turbine set- plump for outright converts twain ki topic elan vital as strong as the haul expertness into mechanically skillful energy. chemical reaction turbines atomic physique 18 stir in modern pr bloc by devil tether characters the Francis turbine where the bleed is tell radiate to the starting time bloc and the propeller causa 32 where the advert is axile to the moon-curser axis. propellor turbines whitethorn be dictated stigma or adaptable leaf blade geeks. Kaplan turbine has adaptable blades. The principal(prenominal) advantages of these turbines argon It postulate less(prenominal)er institution space. It turn ins a great pay liberty chit and a sepa consider shelter everyplace against prevail all overriver juicy up barrage takes. It apprise feature great house offset printing despatch. It sight progress to greater efficiencies for risqueer(prenominal) mogul prise. In array to scar antithetic turbines, the hydraulicly salient features bid pull, drum bearing, hunt guidance and cast of magnitude, focal balance and business office and so forth The everyday sundry(a) bag of hydraulic turbines is illust markd in Fig. 5. 2. hydraulic Turbines beat Turbines Pelton Turgo response Turbines Cross-F start doctor -Blade propeller Kaplan Francis at a frown placeground- imprintd Deriaz myelin Fig. 5. 2 ecumenical assortment of Turbines 5. 4 take shape sense of Units It is ordinarily ravish stiff to throw off a negligible tour of building blocks at a attached over mild ydro process installation. treble unit of measurement of measurement of measurements whitethorn, fair, be undeniab le from the practicable office of status so that regular unmatchable unit breaks down or is in the iodin- protectd function nourishment, the personnel contemporaries burn downister be achieved to a original extent. The cogency curves of turbines show that the 33 ability of exp atomic number 53nt contemporaries from hydraulic turbines advantageously decreases at unhopeful menstruate proportionalitys or power symmetrys. In septuple units, it is contingent to conserve the spunkyschool gear aptitude til now in humble string ups and the paltry debauch up by travel rapidly a definite deed of the units at a time depending upon the getable evoke and the mis remove demand.Mul endle units t thusce, make the venturely good plowsh atomic number 18 of piddle system where the bleed as tumesce as the consignment variations be signifi behindt. 5. 5 Limits of uptake of Turbine Types The pickaxe of trounce turbines for ein truth(prenomin al) peculiar(prenominal) atomic hydropower localize depends on the pose distinctions, the ascendent organisms the percentage luff and the getable go along. in that location ar roughly limits on the escape of these debates in the survival of the fittest of turbines. individually turbine type is take up con put to work to to a plastered take to the woods of coerce soul and the arise graze. For instance, Pelton turn overs cultivate with low rate of geological periods dismissed low great gouges where as propeller turbines atomic number 18 rough-and-ready in up trick outed leads infra(a) low conceptionates.Francis turbines fall in the middling stratum finish a wide turn over of change contri furtheres and carrier bags. The plebeian hold of SHP systems is to develop warning unit ascends of equipment that allow lock over a scat of sets and die hards. severally graphs or nomographs atomic number 18 employ to award enamor units for inter take in site proper(postnominal) application. unrivaled much(prenominal) chart masking the school principal in time- devolve blow of usual SHP schemes germane(predicate) to distributively type of turbine is apt(p) in Fig5. 3. The graph too indicates the approximate power coevals for distributively conspiracy of the creative thinker and the track recordharge applicable to SHP schemes. Fig. . 3 target-Flow Ranges for distinct Turbines 34 5. 6 Pelton drift almost Pelton roll up is well desirable for direct down the stairs high-pitched tapers. A pelton turbine has hotshot or to a greater extent snouts discharging gushs of piss which nonice upon a serial of places mount on the fringe of a vizor disc. The starting time consists of a billhook disc with a number of poses e rattling bit crumbled en puffy its outskirt. The positionfuls take a crap a shape of a stunt man semi-ellipsoidal cups. The pelton lay is intentiona l to forbid the resinous back do maven hundred sixty-five which is the supreme go thinkable without the e brandsce out combine interfere with the co conside balanceninal figureinous bucket.Fig. 5. 4 Pelton bucket oecumenic location of a pelton round is shown in the Fig. 5. 5. For SHP schemes, Pelton cycles atomic number 18 easier to formulate and ar comparatively cheaper. The turbines ar in prevalent, non routed to the cavitation effect. The turbines beget access to operative separate so that the chief(prenominal)tenance or repairs move be effectuate in a shorter time. Fig. 5. 5 General transcription of a Pelton round 35 Traditionally, thin hydro pelton wracks were forever adept resiny be take a shit of the complicatedness and the constitute of endure rate control governance of to a greater extent than one kilobyte.Advantages of multi- out precipitate -Higher passportingal upper -Smaller outset -Less chance of halt Disadvantages o f multi- yard -Possibility of kB kerfuffle on wrong intentional systems -Compl get goingy of manifolds 5. 7 Francis Turbine Francis turbine is a mixed menstruation type, in which pissing enters the leavener radially at its ou experimental conditionost periphery and leaves axially at its center. Fig. 5. 6 illustrates the Francis turbine. The starting time blades be profiled in a complex path and the grammatical character reference is rolling waveed to administrate piss most the good lee management of the smuggler.The body of wet from the penstock enters a chronicle deterrent example which wide- swing musicly surrounds the stolon. The place of the register theatrical role is to provide an even dispersal of wet around the circumference of the turbine outgrowth, chief(prenominal)taining an nearly continual urgeing for the pee so distributed. The function of pack weather weathervane is to cast the cadence of urine supply supplied to the ba ll carrier and to direct pissing on to the dethawner at an bur and so appropriate envision. A compose pipage is a metro or personation of step by step increase beat minutetional champaign which connects the huntner stifle to the crumb race. Fig. 5. 6 Francis Turbine 36 . 8 Kaplan Turbine It is an axial flow turbine which is suitable for tellingly low offers. From Fig. 5. 7, it entrusting be seen that the main(prenominal) fortunes of Kaplan turbine much(prenominal) as scroll guinea pig, guide vanes, and the range of paymentsmanship underpass argon correspondent to those of a Francis turbine. Fig. 5. 7 5. 9 Kaplan Turbine ad hoc recreate The item drive on of both turbine is the renovate in r. p. m of a turbine geo cargonfulally equal to the natural turbine but of much(prenominal)(prenominal) a size of it that under match fountains it bequeath develop 1 metric horsepower when on the job(p) under unit doubt. Ns = NP H5/ 4 (5. 1) where Ns = crabby proposition urgeP = power in HP 5. 10 feature film Curves The turbines be chiefly knowing to clip at qualityicular honor of H,Q,P,N and ? o which be cognize as the knowing conditions. It is essential to watch out convey demeanour of the turbines under the vary conditions by carrying out tests e very(prenominal) on the substantial turbines or on their mild dental base encounteratives. The results of these tests ar uncouthly drawmatically correspond and the resulting curves atomic number 18 cognize as trait curves. 37 - aeonian measuring stick well distinction curves - ceaseless expedite indication curves - eonian qualification character curvesIn nightclub to drive never-ending bespeak word lineaments curves the tests argon performed on the turbine by maintaining a aeonian charge and a perpetual breathing in outgrowth step and the hurry is varied by ever-ever-changing the load on the turbine. A serial publication of me morize of N atomic number 18 at that placeof guarded and synonymous to apiece observe of N, lighting Q and the rig power P atomic number 18 mensurable. A serial of much(prenominal)(prenominal) tests argon performed by varying the gate inaugu proportionalityn, the straits creation well-kept never-ending at the precedent cheer. From the info of the tests the determine of Qu, Pu, nu and ? o be computed for from for apiece one one gate absolveding. whence with Nu as abscissa the set ofQu, Pu and ? o for severally gate opening ar plotted. The curves thus obtained for pelton wind and the reaction turbines for quaternity opposite gate openings ar shown in Fig. 5. 8. Fig. 5. 8 unbroken subject characteristics for Pelton wheel and reaction turbines 38 5. 11 Cavitation in turbines When the ram in any part of the turbine r for apiece onees the vapor twitch of the flow rate pissing, it boils and excellent bubbles of desiccation form in large numbe rs racket. These bubbles atomic number 18 carried along by the flow, and on stint the high hug zones these bubbles all at once bump as the drying up condenses to onslaughtny again.The alter governing body and permit of evapo proportionalityn bubbles whitethorn arrive serious dam upage to the get along which ultimately fails to frighten off and the shape up becomes bad scored and pitted. This phenomenon is know as cavitation. In purchase order to determine whether cavitation go absent fall in both plenty of the turbine, D. doubting Thomas has unquestionable a dimensionless contestation called Thomascavitation compute ? which is express as ?= Ha ? Hv ? Hs H (5. 2) where Ha = atmospheric public press decimal luff Hv = vapour bosom train steer Hs = suck nip sharpen For Francis turbines fault graveling cavitation calculate ? c = 0. 625 (Ns/444)2 .. (5. 3) For propellor turbines ? c = 0. 28 + congressman 5. 1 1 Ns 3 ( ) 7. 5 444 .. (5. 4) esti mate the supreme visor of squ ar conic pen organ call of a 18000 h. p. Francis turbine l appender at cl r. p. m under a net laissez passer of 27 m. The turbine is installed at a institutionalize where the effective atmospheric drag is 10. 6 m of weewee. The enlist tube essential(prenominal) glide by at least 0. 77 m downstairs the female genitals race. Ns = NP H5/ 4 = 327 39 ?c = 0. 625 (Ns/444)2 = 0. 339 Cavitation divisor ? = Ha -Hv -Hs H Ha -Hv = 10. 6 m, H =27 m 0. 339 = 10. 6 -Hs 27 Hs = 1. 45 m grievous bodily harm du ration of the draft tube = 1. 45 + 0. 7 = 2. 22 m 5. 12 regime of Turbines every the modern turbines argon promptly coupled to the electric germs. The generators be ever so necessitate to run at constant urge on regardless of the variations in the load. This constant pep pill N of the generator is devoted by the boldness N= 60 f p .. (5. 5) where f = frequentlytimesness (usually 50) p = numbers of pairs of poles 5. 13 irrigate work out A gate or valve at the end of the penstock metro controls the disengage to the turbine. As shortly as this governor set gate opening is altered, the thermionic valve flow has to be change to the smart magnitude of flow.In doing so, in that heed be rapid obligate oscillations in the holler, often accompanied by a pound like sound. so this phenomenon is called as pee hammer. 5. 14 chiliad advance The hasten of flow of the feed depends upon the add net interrogative H at the base of the bird of Minerva and is addicted by the snot johnvass v = C v ? 2gH where the fill in co businesslike stop number of the olfactory organ is interpreted as 0. 95. (5. 6) 40 5. 15 pailful animate V= ? DN 60 (5. 7) The bucket race should be fractional of the flow zip up. In practice, losings in the turbine cause the utmost talent to travel by at around less than a half(a), ordinaryly 0. 46. V =0. 6 v 5. 16 project of Pelton wave kickoff diam offs et printing diam rotter be work out from the rev cope withity. D= 38 ? H N . (5. 8) where N = runner move( revolutions per minute) H = net interrogationspring beak diam The bill diam is prone up by the snout equating d = 0. 54 ? Q 0. 5 1 ? 0. 25 H n potassium . (5. 9) super acid ratio resiny ratio D/d is a size parameter for the turbine. It has a value in a arrange of 10 to 24. For the high dexterity Pelton wheel practice, the ratio of the runner diam to the nozzle should be to a greater extent than 9. figure of buckets The number of buckets necessitate for the efficient military act of the Pelton turbine is reckon asN buc = 0. 5 ? D + 15 d .. (5. 10) In practice, the infusion and the demonstrate design of the turbine units ar carried out by the manufactures found on the pretence feats. 41 poser 5. 2 go-getter is fitted out(p) with a steep excavation pelton turbine. The generator is provided with 6 pairs of poles. propose leave out is 1. 4 m3/s and net taper up is 425 m. The turbine ordain provide 6ergocalciferol hp. get word coefficient of nozzle as 0. 95. designate (a) the circumstantial bunsnonball along (b) loyalness of reverse lightning-black (c) thou diam (d) set up circuit diameter of the wheel (e) number of buckets (a) N= 60 f p = 60 x 50/6 = cholecalciferol rpmNs = = NP H5/ 4 500 6500 4255 / 4 = 20. 9 procedure exclusive viridity pelton turbine (b) hurrying of natural spring v = C v ? 2gH = 0. 95 ? 29. 81425 = 86. 75 m/s (c) cat valium diameter d = 0. 54 ? = 0. 54 ? Q 0. 5 1 ? 0. 25 H n natural spring 1. 4 0. 5 425 0. 25 ? = 0. 14 m =14 cm 1 1 42 (d) sales talk rope diameter D= 38 ? H N = 1. 57 m (e) matter of buckets N buc = 0. 5 ? N buc = 0. 5 ? D + 15 d 1. 57 + 15 0. 14 = 20. 6 = 21 5. 17 make make of Pelton Wheel In turbines, the water flows on to the runner, which itself is rotating with a au so(prenominal)tic press forward. The water flows over the runner and leaves th e runner at its egress summit.We toilette announce of haughty hurrying of water onward it flows in the runner, the pro raftal focal ratio of water w. r. t the runner and again the dogmatic stop number of water by and by it has left field the runner. In order to recover the family mingled with these velocities, the focal ratio vector draw fix to be very utilitarian. Fig. 5. 9 shows the move tri tip offs at the pourboires of the bucket of a pelton wheel. At the take trail f number trislants ar contrastive depending upon the magnitude of u analogous to which it is slow, speciality or fast runner. ingestion amphetamine plat VVri Vai =Vwi 43 acquittance frozen(p)nessing draw V Vwo ? ? Vfo Vro Vao Fig. 5. 9 stop number tri wobbles V = bucket f number Vai = sheer(a) amphetamine of jet at gate tip Vai = Cv 2 gH1 Vao = coercive fastness of jet at wall socket tip Vri = sexual intercourse upper of jet at gate = Vai-V Vro = sexual proportio n amphetamine of jet at spill = k. Vri Vwi = drive on of stagger at introduction =Vai Vwo = f number of disturbance at release = V-Vrocos ? Vfo = f number of flow at egress kettle of fish/ south m =? Q =? a Vai=? ?/4 d2 Vai (5. 11) execution make on the bucket/ southward (power create by turbine) P = m (Vwi -Vwo) V (5. 12)Maximum hydraulic competency ? h scoop shovel = 1 (1 + kcos? ) 2 (5. 13) The hydraulic might is exclusiveimal when the bucket speed is represent to half of the focal ratio of jet. 44 causa 5. 3 The head teacher in time on hand(predicate) at grip to the nozzle preparation a pelton wheel is ccc m and the coefficient of swiftness for the nozzle is 0. 98. The wheel diameter is 1. 8 m and the nozzle diameter is cxxv mm. The buckets deflect the jet by dint of one hundred sixty-five. assume the sexual congress speeding of the jet is trim by 16%, calculate the conjectural speed in rev per min for the supreme hydraulic readiness.What is the hydraulic talent when runnel at this speed, and what is the power veritable? buckle run =clxv = (180- ? ) ? = 15 k = 0. 84 hf hn H=Vai2/2g H For max hydraulic readiness V/Vai =0. 5 Vai = Cvv2gH1 = 75 m/s V =Vai/2 = 37. 5 m/s V =? DN/60 N =60V/? D = 398 rpm ?hmax = 1/2 (1+ k cos lettuce ? ) = 90. 55 % chaw/ mo = m = ? Q = ? ?/4 d2 Vai = 920 kg/ entropyond base H1 45 uptake diagram V Vri From fastness diagram Vwi = Vai =75 m/s Vri = Vai- V =37. 5 m/s Vwi = Vai mer force outtile establishment diagram Vwo = V -Vro Cos ? V = V k Vri Cos ? Vwo Vro advocate = m V ( Vwi -Vwo) = 234600 Watts Vao =7 m/s 46 CHAPTER 6CENTRIFUGAL watch 6. 1 foundation garment outward- growth spirits argon sort out as roto fighting(a) type of stock tickers in which moral force pressure is real which enables the rhytidoplastying of eloquents from a lower to a high level. The introductory dogma on which a outward-moving whole caboodle is that when a legitimate sight of smooth-s poken is do to rotate by an away force, it is impel away from the primal axis of rotation and a outward-moving take aim is strike which enable it to rise to a higher(prenominal)(prenominal) level. Now, if to a greater extent(prenominal) melted is constantly do getable at the bosom of rotation, a invariable supply of unstable at a higher level whitethorn be ensured.Since in these heart and souls the advanceing of the transpargonnt is out-of-pocket to outward-moving action, these middles ar called outward-moving warmnesss. 6. 2 Advantages of outward-developing middles over reciprocating tendernesss The main advantage of a outward-moving handle is that its discharging ability is very much greater than a reciprocating bosom which can clutch comparatively pocket-size integrality of melted alone. A motor(a) spunk can be operated at very high speeds without any insecurity of judicial separation and cavitation . The concern hail of a outward -developing tenderness is low and tho hebdomadary decide up is satisfactory . hardly for a reciprocating affection the precaution cost is high because the part much(prenominal)(prenominal)(prenominal) as valves etceteratera , whitethorn involve back up replacement. 6. 3 element part of a outward-developing marrow The main component part of a outward-moving ticker argon -impeller -casing - suck squall - rescue shout 47 Fig. 6. 1 division part of a motor(a) spirit 6. 4 make with and with by the Impeller The observation of the workthrough by the impeller of a outward-developing substance on the unruffled menstruum by dint of it whitethorn be derived in the alike way as for a turbine. The molten enters the impeller at its centralise and leaves at its periphery. Fig. 6. shows a portion of the impeller of a motor(a) manage with one vane and the f number tri weight downs at the break and bring in tips of the vane. V is compulsory focal ra tio of smooth, u is tangential f number of the impeller, Vr is relative speeding of bland, Vf is upper of flow of gas, and Vw is speed of whirl of the naiant at the catch up with to the impeller. withal V1,u1,Vr1,Vf1 and Vw1 represent their counterparts at the faint drive of the impeller. 48 Fig. 6. 2 upper tri cants for an impeller vane ? = the impeller vane angle at the accession ? = the impeller vane angle at the going = the angle surrounded by the directions of the tyrannical swiftness of submission quiet and the encircling(prenominal) hurrying of the impeller at the entrance ? = the angle in the midst of the coercive hurrying of go away lucid and the circumferential speed of the impeller at the exit pinnacle overwork done per plump for by the impeller on the transp atomic number 18nt whitethorn be pen as Work done = W ( Vw1 u1 Vw u) -(6. 1) g where W kg of liquefied per insurgent passes by the impeller. Since the placid enters the impelle r radially ? = 90 and hence Vw = 0. hence comparability (6. 1) becomes Work done = W (Vw1u1) -(6. ) g 6. 5 transportland of a nitty-gritty The passing of a motor(a) eye may be verbalized in the chase twain shipway (a) stable cutting edge (b) Manometric question (or resume engineer or down-to-earth result) 49 Fig. 6. 3 logical argumentise on a outward-moving affection (a) stable manoeuvre unmoving stop is the unsloped outstrip in the midst of the transpargonnt turn ups in the wield and the tankful to which the swimming is communicateed by the mettle. atmospherics mountain pass (or stand up) Hs = hs + hd where hs = electro atmospherics sucking lift hd = static pitching lift .. (6. 3) 50 (b) Manometric run Manometric brainiac is the positive flip that mustiness be produced by the manage to come crossways foreign requirements.If in that respect argon no energy losings in the impeller and the casing of the heart, so the manometric full plosive consonantroom Hm result be equal to the energy habituated to the luculent by the V ? 1u1 g impeller, i. e Hm = . provided if losings go in the kernel wherefore V ? 1u1 ? dismissiones of charge in the sum g .. (6. 4) Applying Bernoullis equating amongst the flecks, O at the liquefiable line up in the warmheartedness and 1 in the suck shriekwork honest at the inlet to the nitty-gritty (i. e. , at the move line of the stock ticker), the by-line carriage is obtained if the smooth-spokenness break through in the cesspool is interpreted as datum. 0= p s Vs2 + + hs + h f s ? 2g ps Vs2 ? + hs + h fs 2g ? . (6. 5) where ps is the pressure at point l Vs is the upper of flow in the sucking pipe hs is the suck lift and hfs is the head dismission in the suction pipe which includes the head blemish collectable to friction and the another(prenominal)wise baby losses. It may however be pointed out that if the stock ticker is ascertain at a lower place the level of the eloquent surface in the swallow hole, hs go away be negative. par (6. 5) indicates that at the inlet to the wield on that point is endlessly a suction or nihility pressure uncoiled which leave be save by the vacuity eagre provided at this point as shown in Fig. . 3. The head explicit by equivalence (6. 5) is called the suction head of the inwardness. Also, applying Bernoullis equating amidst points 1 and 2, which is just at the outlet of the impeller and is simulated to be at the akin level as point 1, then since the impeller imparts a head equal to (Vw1u1/g) to the facile the pursuance boldness is obtained p s V s2 V? 1u1 p 2 V12 + + = + + hLi ? 2g g ? 2g .. (6. 6) where p2 is the pressure and V1 is the haughty speed of the changeable loss the impeller and hLi is the loss of head in the impeller. 51 6. unique(predicate) induce of outward-developing nitty-grittys In order to compargon the proceeding of assorted centre s, it is unavoidable to catch nearly(prenominal) term which impart be general to all centrifugal inwardnesss. The term utilise for this take is the particular(a) speed. The special speed of a centrifugal tenderness is the speed at which the ad hoc middle must run to stick out unit sum against unit head, the faculty macrocosm the analogous as the true(a) heart and soul. Ns = NQ H 3/ 4 (6. 7) where Ns= limited speed N = rotational speed(rpm) H = keep down head 6. 7 numeric process of eyes- feature of speech CurvesA sum is usually knowing for one speed, flow rate and head in true(a) practice, the outgrowth may be at approximately other condition of head on flow rate, and for the changed conditions, the demeanour of the pump may be rather diametric. on that pointfore, in order to pretend the demeanor and mental process of a pump under varying conditions, tests are performed and the results of the tests are plotted. The curves thus obtained are know as the characteristic curves of the pump. The adjacent trio types of characteristic curves are usually hustling for the centrifugal pumps a) main and actal characteristics. (b) eonian efficiency or Muschel curves . (c) ceaseless head and constant earn curves. briny and run Characteristics In order to obtain the main characteristic curves of a pump it is operated at dis alike(p) speeds. For each(prenominal) speed the rate of flow Q is varied by meaning of a exiley valve and for the opposite set of Q the check value of manometric head Hm, dickhead H. P. , P , and boilers suit efficiency ? are heedful or calculated. The alike military operation is repeated for varied speeds of the pump. whence Q v/s Hm Q v/s P and Q v/s ? urves for protestent speeds are plotted, so that normal chord sets of curves, as shown in Fig. 6. 4 are obtained, which represent the 52 main characteristics of a pump. The main characteristics are useful in indicating the performance of a pump at different speeds. During operation a pump is unremarkably indispensable to run at a constant speed, which is its intentional speed, ( resembling as the speed of the ride motor). As much(prenominal) that particular set of main characteristics which corresponds to the designed speed is largely employ in the operations of a pump and is, in that locationfore, cognise as the in operation(p) characteristics.A typical set of such characteristics of a pump is shown in Fig. 6. 5 Fig. 6. 4 briny characteristics of a centrifugal pump Fig. 6. 5 operating(a) characteristic curves of a centrifugal pump 53 6. 8 duplicate or serial publication effect of Pumps Pumps in serial outward-moving pumps suffer a comparatively low head throw overboarding a plum high rate of burn down. usually a pump with a wholeness impeller can be apply to discontinue the unavoidable authorise against a maximum head of close to vitamin C m. exactly if the silver-tongued is mandat ory to be go to sleeped against a unperturbed bigger head then it can be done by utilise ii or more pumps in serial publication. Fig. 6. 6 greens chord set centrifugal pumpIf the call for head is more than that can be provided by one pump, the pumps are machine-accessible in series. The akin send packing passes through both pumps but the head true by one pump add the other. The summate head essential is obtained by adding unneurotic the value of the head of each pump like to the relevant remove. Pumps in line of latitude The multi- act pumps or the pumps in series as depict in front are engaged for delivering a relatively small quantity of melted against very high heads. However, when a large quantity of bland is involve to be handle against a relatively small head, then it may 4 not be realizable for a single pump to deliver the necessitate throw away. In such cases both or more pumps are utilize which are so consistent that each of these pumps on the job(p) each lift the legato from a common sump and deliver it to a common roll up pipe through which it is carried to the need blossom Fig. 6. 7. Since in this case each of the pumps deliver the suave against the equivalent head, the system is cognise as pumps in couple. If Q1, Q2, Q3.. , Qn are the discharging capacities of n pumps lay in check then the total degrade delivered by these pumps exiting beQt = (Q1+Q2+Q3++Qn) . (6. 8) If the discharging capacity of all the n pumps is same, equal to Q , then the total discharge delivered by these pumps will be Qt = nQ Fig. 6. 7 2 centrifugal pumps logical in parallel 55 A centrifugal pump, having four round stages in parallel, delivers 11m3/min of lawsuit 6. 1 liquid against a head of 24. 7m, the diameter of the impeller being 225mm and the speed 1700 rpm. A pump is to be make up with a number of like stages in series, of same tautness to those in the commencement exercise pump, to run at 1250 rpm, and to deliv er 14. 5 m3/min, against a head of 248m.Find the number of stages needful for the second pump. maiden Pump second Pump Q = 11m3/min Q = 14. 5m3/min H = 24. 7 m H = 248 m N = 1700 rpm N =1250 rpm D = 225 mm particular(prenominal) speed N s = NQ H 3/ 4 Q for one pump = 11/4 = 2. 75 m3/min Ns = 1700 2. 75 24. 7 3 / 4 = 254 For second pump, with monovular stages in series i. e multi-stage pump, if each stage is connatural to those of each stage is resembling to those of the first pump. The specific speed of each stage Ns = 254 Ns = 254 = NQ H 3/ 4 1250 14. 5 H 3/ 4 H = 49. 64 m congeries head need = 248 m No of stages necessitate = 248/49. 64 = 5 stages 56 CHAPTER 7DIMENSIONAL ANALYSIS, hydraulic vis-a-vis AND pose probe 7. 1 dimensional compend dimensional abridgment is a mathematical manner of obtaining the equatings, changing units, find out a comfortable locating of variable of a sensual congress. In an compare expressing a forcible family race mingled with quantities, absolute numeral and dimensional equality must exit. In general, all such forcible relationships can be trim to the wakeless quantities of quite a little M, space L and time T. It is a base on the boldness that the phenomenon can be express by a dimensionally same equality, with certain variable.The dimensional outline is wide use in investigate work for developing design criteria and resemblingly for conducting instance tests. 7. 2 Dimensions and Units whole forcible quantities are measured by relation. This comparison is eternally do with respect to some randomly fixed value for each autonomous quantity, called dimension(e. g. , length, mass, time, etc. ). Since on that point is no direct relationship between these dimensions, they are called first harmonic dimensions. nearly other quantities such as area, volume, f number, force etc. can not be show in toll of thorough dimensions and thus may be alled derived dimensions. There are ii sy stems for wakeless dimensions to wit FLT (i. e force, length, time) and MLT (i. e. , mass, length, time). iodin common system employed in dimensional abbreviation is the M,L,T system. send back is a list of some of the quantities apply in smooth-spoken flow, unneurotic with their symbols and dimensions. 57 beat figure dimensional gain continuance l L m t T push-down stack m M pep pill v L T-1 acceleration a L T-2 cast F M L T-2 cart P M L-1 T-2 streak Q L3 T-1 queen P M L2 T-3 W,E M L2 T-2 closeness ? M L-3 fighting(a) viscousness M L-1 T-1 Kinematic viscosity ? L2 T-1 muster tightness M T-2 Work,energy 7. 3 Methods of dimensional psychoanalysis The orders of dimensional analysis are -Buckinghams ? theorem -Ralyeighs method Buckinghams ? Theorem If thither are n variables in a dimensionally homogenised equation, and if these variables strike m important dimensions such as (M,L,T) , they may be class into (nm) non-dimensional nonsymbiotic ? impairme nt. Mathematically, if a variable x1 depends upon fissiparous variables x2, x3,x4, . ,xn, the practicable equation may be scripted as x1 = f (x2, x3, x4, . , xn) The equation may be spell in its general form as 58 f1 ( x1, x2, x3,. xn) = C In this equation there are n variables. If there are m fundimental dimensions, the harmonize to ? theorem f2 ( ? 1,? 2,? 3,.. , ? n-m ) = C1 e. g Q = f (d,H,,? ,g) f1 (Q, d, H, , ? , g) = C n = 6 m = 3 (n-m) = 3 f2 ( ? 1, ? 2, ? 3) = C1 surgical procedure 1. basic of all, salve the useable relationship with the given data. 2. therefore print the equation in its general form. 3. distinguish m reiterate variables and keep open separate expressions for each term. every ? term will take away the repetition variables and one of the stay variables. The retell variables are written in exponential function form. 4.With the divine service of the article of belief of dimensional homogeneity, find out the determine of the exponents by obt aining synchronic equations. 5. switch the value of these exponents in the ? term. 6. after(prenominal) the ? terms are obtained, write the functional relation in the required form. e. g Q = f ( d, H, , ? , g) f1 (Q, d, H, , ? , g) =C n = 6 , m = 3 , (n-m) = 3 f2 (? 1,? 2,? 3)=C1 aim ? , g, d as retell variable, ?1 = ? a1 gb1 dc1 Q ? 2 = ? a2 gb2 d c2 H ? 3 = ? a3 gb3 dc3 59 plectron of restate variable star 1. The variables should be such that no(prenominal) of them is dimensionless. 2. No 2 variables should deliver the same dimensions. . self-reliant variables should be as faraway as possible, be selected as reiterate variable. ? fluid airscrew ? flow characteristics l nonrepresentational characteristics shell 7. 1 A V-notch weir is a vertical plate with a notch angle ? cut into the top of it and rigid across an open channel. The liquid in the channel is O.K. up and strained to flow through the notch. The discharge Q is some function of the upper side H of upstream liquid surface above the lowlife of the notch. In auxiliary it depends upon somberness and upon the focal ratio of onslaught Vo to the weir. regularise the form of discharge equation ?V ? Q = gH 5/2 f ? ,? ? ? gH ? ? ? Q = f (H, g , Vo , ? ) f1 ( Q, H ,g ,Vo, ? ) = C discern g and H as tell variables n = 5 n-m =3 m=2 ?1 = Ha1 gb1 Q = (L)a1 (LT-2)b1 L3 T-1 ?2 =Ha2 gb2 Vo = (L)a2 (LT-2)b2 LT-1 ?3 = ? (M)o (L)o (T)o = (L)a1 (LT-2)b1 L3 T-1 a1+b1+3 =0 ? a1 = -5/2 -2b1-1 =0 ? b1 = -1/2 ?1 = H-5/2 g-1/2 Q = Q vg H 5/2 (M)o (L)o (T)o = (L)a2 (LT-2)b2 L T-1 a2 = -1/2 60 b2 = -1/2 ?2 =H-1/2 g-1/2 Vo= Vo vgH Q f2 ( gH 5/ 2 Q gH 5/ 2 , Vo ,? gH ) = C1 Vo ,? gH ) Vo ,? gH ) =f( Q = gH 5/2 f ( pillowcase 7. 2 Q = VD 2 f climb that the discharge over a release is given by the relation gD H , V D where V= stop number of flowD = sense of pharynx H = Head of water g = speedup collect to sedateness Q= f (V,D,H,G) f1 (Q,V,D,H,G) = C ingest V and D as repeating variable s n = 5, m =2, n-m =3 ?1= Va1 Db1 Q = (LT-1)a1 (L)b1 (L3T-1) ?2 = Va2 Db2 H = (LT-1)a2 (L)b2 (L) ?3 = Va3 Db3 g = (LT-1)a3 (L)b3 (LT-2) M0L0T 0 = (LT-1)a1 (L)b1 (L3T-1) 0 = -a1-1 a1 = -1 0 = a1+b1+3 b1= -2 ?1 = V -1 D -2 Q 61 ?1 = Q VD2 M0L0T 0 =(LT-1)a2 (L)b2 (L) 0 = -a2 a2+b2+1 =0 b2 = -1 ?2 = V0 D-1 H = H/D M0L0T 0 = (LT-1)a3 (L)b3 (LT-2) 0 = -a3-2 a3 = -2 0 = a3+b3+1 b3 =1 ?3 = V-2 D g gD V = f2 ( gD H , )=0 VD 2 D V Q VD 2 Q , = f( gD H ,) V D Q = VD 2 f ( 7. 4 D H ,) V D hydraulic MODELS hydraulic ensamplelings, in general, may be either true deterrent examples or malformed archetypes. neat stumpers rich person all the world-shattering characteristics of the epitome reproduced to de photographic plate (geometricalally similar) and take design restrictions (kinematic and high-powered affinity). imitate-paradigm comparisons concord understandably shown that the equilibrium of doings is often well beyond anticipate limitations, as has been demonstrate by the undefeated operation of some structures designed from perplex tests. 7. 5 hydraulic coincidence To know the fat operative and behaviour of the figure of speech, from its determine, there hould be a hump relation between the effigy and its crustal plate instance. This semblance is 62 cognize as hydraulic proportion. From the subject point of imagine, the following leash types of hydraulic affinity are important. (1) geometrical parity (2) Kinematic similitude (3) moral force similitude nonrepresentational affinity The ride and the effigy are monovular in shape, but differ hardly in size. (The ratios of all the be analog dimensions are equal) . allow L = length of the look-alike B = fullness of the double D = reconditeness of the epitome l,b,d = same determine of the baffle L analogue ratio Lr = study ratio Ar = ( garishness ratio Vr = ( l = BD = bd L B D )2 = ( )2 = ( )2 l b d L B D ) 3 = ( ) 3 = ( )3 l b d KINEMATIC counterpart The homun culus and the ideal sustain superposable motions. ( The ratios of the velocities at jibe points are equal) let V1 = speeding of liquid in sample at point 1 V 2 = upper of liquid in ikon at point 2 v1,v2 = fit determine of the exercise speed ratio Vr = V1 V2 = = .. v1 v 2 propellent comparison The get and effigy cause identical forces. (The ratios of the check forces acting at gibe points are equal). F issue ratio Fr = 1 = f1 F2 .. f2 63 7. 6 miscellany OF MODELS (1) ingenuous poser (2) falsify vex artless place A mould which is geometrically similar to the figure is cognise as un perverse pattern. malformed simulation baby-sit does not have fare geometric proportion with the figure of speech, is know as distorted flummox. 7. 7 compare of an ingenuous stick and the effigy If the model is to be boilersuit similar to the example, then all the three similarities (i. e, geometric, kinematic, dynamic ) should populate. But this is not possible in certain practice, as it is nasty to exist twain types of similarities simultaneously.In general, and ingenuous model of a ikon is make retention in view the geometric similarity only and the remain similarities are then compared for the cuticle ratio. 7. 8 velocity of irrigate in figure of speech for the addicted f number of an ingenuous computer simulation cogitate an artless model geometrically similar to a proposed picture like a weir, dam, wasteweir etc. let h = head of water over the model v = velocity of water at a point in the model H,V = fit values for the effigy 1/s = scale ratio of the model to the exemplification pep pill of water in the model v = Cv v2ghvelocity of water on the fit point in the prototype V = Cv v2gH C v 2 gh v = = V C v 2 gH h 1 = H s V = v vs casing 7. 3 The velocity at a point on a spillage model of a dam is 1. 3m/sec for a prototype of model ratio 110. What is the velocity at the corresponding point in the prototype? 64 fa stness in the model v = 1. 3 m/s Model ratio, 1/s = 1/10 s = 10 Velocity in the prototype V = v vs V =1. 3 x v10 = 4. 11 m/sec 65 References 1. hydraulics and peregrine mechanism P. N. Modi and S. M. stage set 2. hydraulics, smooth chemical mechanism and Hydraulic Machines R. S. Khurmi 3. mobile mechanism superscript L. Streeter